A study of SIQR model with Holling type–II incidence rate

Abstract

In this study, we propose an SIQR epidemic model with a Holling type-II incidence rate. In this model, the
total population N is divided into five compartments; namely susceptible individual class (S), infective individual
class (I), quarantine from susceptible individual class (Q1), quarantine from infective individual class (Q2), and
recovered individual class (R). The basic reproduction number (R0) of the model is found by the next generation
method and then disease-free (DF) and endemic equilibrium points of the system are found and their existence
conditions are presented. This study concludes that if the basic reproduction number R0 is less than one, the
disease-free equilibrium is globally asymptotically stable and if the basic reproduction number R0 is greater
than one, then the endemic equilibrium exists and globally. In this study, we also discuss the behavior of the
disease-free equilibrium points by using manifold theory when the basic reproduction number R0 is equal to one.
This study is very helpful in those pandemic diseases wherein the quarantine process of an infected individual is
one of the most effective solutions to get recover from the disease and also to control the spreading of disease
from an infected individual to uninfected individuals. The numerical simulation is given, and to analyze the found
results, at the last conclusion is also given.